Adjusted and Unadjusted Beta

Betas calculated purely based on historical data are unadjusted betas. However, this beta estimate based on historical estimates is not a good indicator of the future. This is also called the beta instability problem.

Statistically, over time betas may exhibit mean reverting properties as extended periods significantly above 1 (one) may eventually decline and betas below one may revert toward 1.

Therefore analysts may apply models to create an adjustment calculation for the historical beta and use this adjusted beta to calculate the expected return for the security.

The generalized formula for adjusted beta can be presented as follows:

Adjusted Beta Β = α₀ +α_1Βi,t-1

Where, α₀ + α₁ = 1

Because of the mean reverting property of beta, the adjusted beta will move closer to 1. If the historical or unadjusted beta is greater than 1, then the adjusted beta will be lesser that unadjusted beta and closer to 1, and vice versa.

Let’s take an example to understand this.

Assume that the historical beta for a company is 1.5. the adjusted beta formula for the company is 3/4 + 1/4 Βt-1

Adjusted beta = 3/4 + 1/4 * 1.5 = 1.125

The larger the value of α0, the faster the adjusted beta will move towards 1.

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Adjusted and Unadjusted Beta

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The Market Model for a Security’s Returns

Multifactor Models

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